Open Access

The square-transform of Hermite-Biehler functions. A geometric approach

Abstract

We investigate the subclass of symmetric indefinite Hermite-Biehler functions which is obtained from positive definite Hermite-Biehler functions by means of the square-transform. It is known that functions of this class can be characterized in terms of location of their zeros. We give another, more elementary and geometric, proof of this result. The present proof employs a shifting-of-zeros' perturbation method. We apply our results to obtain information on the eigenvalues of a concrete boundary value problems.

Article Information

 Title The square-transform of Hermite-Biehler functions. A geometric approach Source Methods Funct. Anal. Topology, Vol. 13 (2007), no. 2, 187-200 MathSciNet MR2336721 Copyright The Author(s) 2007 (CC BY-SA)

Authors Information

Vyacheslav Pivovarchik
Department of Applied Mathematics and Informatics, South-Ukrainian State Pedagogical University, 26, Staroportofrankovskaya, Odessa, UA-65091, Ukraine

Harald Woracek
Departement for Analysis and Scientific Computing, Vienna University of Technology, Wiedner Hauptstr. 8-10/101, A-1040 Wien, Austria

Citation Example

Vyacheslav Pivovarchik and Harald Woracek, The square-transform of Hermite-Biehler functions. A geometric approach, Methods Funct. Anal. Topology 13 (2007), no. 2, 187-200.

BibTex

@article {MFAT405,
AUTHOR = {Pivovarchik, Vyacheslav and Woracek, Harald},
TITLE = {The square-transform of Hermite-Biehler functions. A geometric approach},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {13},
YEAR = {2007},
NUMBER = {2},
PAGES = {187-200},
ISSN = {1029-3531},
URL = {http://mfat.imath.kiev.ua/article/?id=405},
}`